Hawkeye you are right about these funny French-breds! They are referred to AQPS (Autre Que Pur-Sang - "Other than pure blood"). They are basically a cross between Thoroughbreds and traditional French breeds, but the criteria is that they must be 80% Thoroughbred to be allowed to race.
The BHA allows them to run in the UK on the proviso that their pedigree has been verified by the French authorities.
Previously AQPS horses were not allowed to run in restricted "National Hunt" races (those only open to horses which have not run under Flat rules) in the UK, as many of them had run in special AQPS races in France. The rules were changed in 2008 to recatagorise AQPS only Flat races in the same category as Bumpers, thus allowing them to run in more races in the UK.